Abstract
The inventory models considered so far are all deterministic in nature; demand is assumed to be known and either constant over the infinite horizon or varying over a finite horizon. In many logistics systems, however, such assumptions are not appropriate. Typically, demand is a random variable whose distribution may be known.
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References
Archibald, B., & Silver, E. A. (1978). (s, S) policies under continuous review and discrete compound Poisson demand. Management Science, 24, 899–908.
Arrow, K., Harris, T., & Marschak, J. (1951). Optimal inventory policy. Econometrica, 19, 250–272.
Bell, C. (1970). Improved algorithms for inventory and replacement stock problems. SIAM Journal on Applied Mathematics, 18, 558–566.
Chen, Y. F. (1996). On the optimality of (s, S) policies for quasiconvex loss functions. Working Paper, Northwestern University.
Chen, F., & Zheng, Y. S. (1994). Lower bounds for multi-echelon stochastic inventory systems. Management Science, 40, 1426–1443.
Clark, A. J., & Scarf, H. E. (1960). Optimal policies for a multi-echelon inventory problem. Management Science, 6, 475–490.
Denardo, E. V. (1996). Dynamic programming. In Avriel, M., Golany, B. (Eds.), Mathematical programming for industrial engineers (pp. 307–384). Englewood Cliffs, NJ: Marcel Dekker.
Eppen, G., & Schrage, L. (1981). Centralized ordering policies in a multiwarehouse system with lead times and random demand. In L. Schwarz (Ed.) Multi-level production/inventory control systems: theory and practice. Amsterdam: North-Holland.
Federgruen, A., & Zipkin, P. (1984a). Approximation of dynamic, multi-location production and inventory problems. Management Science, 30, 69–84.
Iglehart, D. (1963a). Optimality of (s, S) policies in the infinite horizon dynamic inventory problem. Management Science, 9, 259–267.
Iglehart, D. (1963b). Dynamic programming and stationary analysis in inventory problems. In H. Scarf, D. Guilford, M. Shelly (Eds.) Multi-stage inventory models and techniques (pp. 1–31). Stanford, CA: Stanford University Press.
Lee, H. L., & Nahmias, S. (1993). Single product, single location models. In S. C. Graves, A. H. G. Rinnooy Kan, P. H. Zipkin (Eds.) Handbooks in operations research and management science, the Volume on Logistics of production and inventory (pp. 3–55). Amsterdam: North-Holland.
Pang, Z. (2011). Optimal dynamic pricing and inventory control with stock deterioration and partial backordering. Operation Research Letter, 39, 375–379.
Porteus, E. L. (1990). Stochastic inventory theory. In D. P. Heyman, M. J. Sobel (Eds.) Handbooks in operations research and management science, the volume on Stochastic models (pp. 605–652). Amsterdam: North-Holland.
Ross, Sheldon M. (1983). Introduction to Stochastic Dynamic Programming. Academic Press, INC., London.
Ross, S. (1970). Applied Probability models with optimization applications. San Francisco: Holden-Day.
Rosling, K. (1989). Optimal inventory policies for assembly systems under random demand. Operation Research, 37, 565–579.
Scarf, H. E. (1960). The optimalities of (s, S) policies in the dynamic inventory problem. In K. Arrow, S. Karlin, P. Suppes (Eds.) Mathematical methods in the social sciences (pp. 196–202). Stanford, CA: Stanford University Press.
Veinott, A. (1966). On the optimality of (s, S) inventory policies: new condition and a new proof. Journal SIAM Applied Mathematics, 14, 1067–1083.
Veinott, A., & Wagner, H. (1965). Computing optimal (s, S) inventory policies. Management Science, 11, 525–552.
Zheng, Y. S. (1991). A simple proof for the optimality of (s, S) policies for infinite horizon inventory problems. Journal of Applied Probability, 28, 802–810.
Zheng, Y. S., & Federgruen, A. (1991). Finding optimal (s, S) policies is about as simple as evaluating a single policy. Operation Research, 39, 654–665.
Zipkin, P. H. (2000). Foundations of inventory management. Burr Ridge, IL: Irwin.
Zipkin, P. H. (2008). On the structure of lost-sales inventory models. Operation Research, 56, 937–944.
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Simchi-Levi, D., Chen, X., Bramel, J. (2014). Stochastic Inventory Models. In: The Logic of Logistics. Springer Series in Operations Research and Financial Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9149-1_9
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